Median filters are widely used in image processing because they remove impulsive noise while preserving edges and locally monotonic regions. Median filters are one example of a class of filters known as order statistic filter that require a ranking of pixels within the filter window. When only one of the ordered pixels (the ith pixel) is selected as the output of the filter, the result is called an ith ranked-order operation. The median filter of window size N is therefore an (N+1)/2 ranked-order operation. Maximum and minimum filters are respectively Nth and 1st ranked-order operations. Such filters have been applied to texture and feature analysis as well as noise reduction. When utilized on binary images, a minimum filter results in an operation known as erosion, and a maximum filter results in dilation. Successive applications of erosion and dilation result in morphological transformations that are useful for image segmentation.
Ranked-order filters begin with a ranking of the pixels within the filter window. Various algorithms have been presented for performing this nonlinear neighborhood operation. Threshold decomposition (as explained by J. P. Fitch, E. J. Coyle, and N. C. Gallagher, Jr., "Median Filtering by Threshold Decomposition," IEEE Trans. on Acoustics, Speech, and Signal Proc. ASSP-32, 1183 (1984)) is an approach that transforms the ranking operation to a linear space-invariant filtering step followed by a nonlinear point-to-point threshold comparison step. Threshold decomposition separates a (K+1)-level quantized input image into K binary threshold images. (For example, 16 binary images will encode a 17-level image; for notational convenience, this is referred to as a K-level decomposition.) This kth threshold image is 1 where the input image exceeds the kth input threshold of the equalizer and 0 elsewhere. Ranked-order filtering of the binary threshold images can be realized with a moving average followed by a global threshold comparison step. Superposition of the K ranked-order filtered threshold images yields the filtered output image.
An analog optical electronic system which performs ranked-order operation of binary images only has been disclosed in the following: K. S. O'Neill and W. T. Rhodes, "Morphological Transformations by Hybrid Optical-Electronic Methods," Proc. SPIE 638, 1986. Implementation of this system is based on an incoherent imaging system whose point spread or blurring function is the desired filter function.
Electronic means of determining threshold levels across an image for use in converting the analog pixel signals into digital pixels have been disclosed in U.S. Pat. No. 4,442,544 (Moreland et al) and U.S. Pat. No. 4,468,704 (Stoffel et al). These pixel values are then either stored or sent to a device such as a printer.